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ma174_hw1 - Assigned Friday Sep 23 2011 Due Friday Sep 30...

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Assigned: Friday, Sep. 23, 2011 Due: Friday, Sep. 30, 2011 MATH 174/274: Homework 1 “Taylor Series and Round-Off Error” Fall 2011 1. Compute the first 5 terms in the Taylor series (constant, linear, quadratic, cubic, and quartic pieces) for the following functions: (a) f ( x ) = 4 x - x 2 , about the point x = 2 (b) f ( x ) = 3 tan( x ), about the point x = π/ 4 2. Using the results from Problem 1(a), make a single MATLAB plot which contains all of the following: (a) a graph of f ( x ) = 4 x - x 2 versus x for x (0 , 4). (b) a graph of p 0 ( x ). (c) a graph of p 2 ( x ). (d) a graph of p 4 ( x ). (e) a title, x -axis label, y -axis label, and a legend. 3. The quotient g ( x ) = log(1 + xe x ) x seems at first glance to be undefined at x = 0. Approximate log(1+ xe x ) by a Taylor polynomial of degree 2 about the point x = 0. Use this Taylor approximation to determine a natural definition of g (0). 4. Consider the function f ( x ) = 1 / (1 - x ). (a) Obtain the infinite Taylor series representation of f ( x ) about the point x = 0.
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